If you’re shooting above normal flash sync speed, then in most cases yes: any flash contributing to the exposure needs to support HSS. A non-HSS strobe fired at high shutter speeds will usually be partially blocked by the shutter, which can cause banding or only a strip of light in the frame.

So:

• HSS main light + non-HSS fill/hair light at high shutter speed: usually problematic.
• HSS main light + reflector: fine, since a reflector isn’t a flash.
• HSS main light + constant light: can work, since continuous light isn’t limited by flash sync the same way.

If you want to use non-HSS strobes together with your main light, a common workaround is to stay at or below your camera’s normal sync speed. You can also use a neutral density filter to reduce ambient light so you don’t need the faster shutter speed.

In short: for a fully flash-based setup above sync speed, plan on all participating flashes being HSS-capable.